The name on the direct debit doesn't need to change, if you're wanting this to change we would need to submit another direct debit mandate.

If you want this to happen I can call you to discuss this.

And a warning to the OP - if you do decide to set up a new DD mandate, don't do it within 10 days of a payment being due, otherwise you are likely to get stung with an additional £1.50 (I think) charge for paying by another method. Personally, I'd leave it as it is.